Existence and stability of curved fronts for spatially periodic combustion reaction-diffusion equations in $\mathbb{R}^N$

Wei-Jie Sheng; Xin-Tian Zhang

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arXiv · 2510.21163

Existence and stability of curved fronts for spatially periodic combustion reaction-diffusion equations in $\mathbb{R}^N$

Wei-Jie Sheng·Xin-Tian Zhang

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Abstract

This paper is concerned with curved fronts of combustion reaction-diffusion equations in spatially periodic media in $\mathbb{R}^N$ $(N\geq2)$. Under the assumption that there are moving pulsating fronts for any given propagation direction $e \in \mathbb{S}^{N-1}$, and by constructing suitable super- and sub-solutions, we prove the existence of a curved front with polytope-like shape in $\mathbb{R}^N$. Then we show that the curved front is unique and asymptotically stable.

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Wei-Jie Sheng, Xin-Tian Zhang. 2025-10-24. Existence and stability of curved fronts for spatially periodic combustion reaction-diffusion equations in $\mathbb{R}^N$. https://arxiv.org/abs/2510.21163

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